I am often asked by the students I tutor, “What is the best way to prepare for TMUA?” and “How do I do well in TMUA?”. As a result, having sat TMUA myself, achieving a 9 in paper 1 and 8.4 overall, plus tutoring the entrance exam for the last few years, I decided to write the following article in hopes of helping other students who may be wondering the same thing.

1. Work through the 'Notes on Logic and Proof'

‘Notes on Logic and Proof’ is a pdf document written by Cambridge Assessment Admissions Testing. It introduces and works through the mathematical logic and methods of proof which you need to be comfortable with when sitting TMUA. I recommend having a pen and paper beside you as you read and work through the examples and exercises yourself. This is best done before you begin attempting Paper 2, since this knowledge of logic and proof is assumed and comes up frequently in questions.

The content assessed in the MAT exam aligns closely with the specification for TMUA. In section 1 of the MAT papers, there are 10 challenging multiple choice questions, based on the content of first year A Level Maths (with a couple of topics from second year A Level Maths), and as a result are an excellent way to practice the techniques needed for TMUA’s multiple choice questions. This way you can get used to the unusual style of question whilst saving the limited number of TMUA papers for a later stage of your preparation.

Of all the many textbooks I have tried, this one stands out due to the challenging multiple choice questions which are similar to those at the end of the TMUA papers and so can really help you excel in your TMUA preparation. There are worked solutions to all the questions online here:

The final way to prepare for TMUA is by doing past papers.

Paper 1 should be accessible without having worked through the Notes on Logic and Proof.

When working through the past papers, I would advise to start with the oldest, such as the practice papers and the specimen papers. I would suggest not working through these under timed conditions but instead taking your time to work through the questions, getting used to the style of the multiple choice and spending a good amount of time on each question to problem-solve. That way, you concentrate on getting more correct answers over how quickly you finish the paper. Once done, mark your answers straight after and look at a worked solution for any you got wrong. Work through it step-by-step so that you thoroughly understand how to get to the answer which will enable you to improve each time you tackle a past paper.

Once you feel confident with the style of questions, then practise the remaining past papers under timed conditions. This will allow you to gauge what sort of pace you need to work at in order to have enough time to answer each question in the exam. You need to find a balance where you are not rushing, but neither are you taking too long on each question. You should find your pace of working through the questions will naturally increase with practise since you likely will feel more comfortable and confident.

TMUA is a challenging admissions test – even with thorough preparation, it is not unusual to struggle with the style of question since they are unlike what you are used to seeing in school.

If you would like to enhance your exam technique, mathematical intuition, problem-solving skills and efficiency for TMUA, I offer one-to-one tuition. You can find more information on this here: